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Hypothesis Testing-Chi-Square Test ,[object Object],SHAMEER P.H,[object Object],dept. of futures studies 2010-'12,[object Object]
REWIND YOUR MIND,[object Object],Hypothesis-,[object Object],[object Object]
normal question that intends to resolve
tentative formulated for empirical testing
tentative answer to research question
point to start a researchdept. of futures studies 2010-'12,[object Object]
Research Questions and Hypotheses,[object Object],Research question:,[object Object],Non-directional:,[object Object],No stated expectation about outcome,[object Object],Example:,[object Object],Do men and women differ in terms of conversational memory?,[object Object],Hypothesis:,[object Object],Statement of expected relationship,[object Object],Directionality of relationship,[object Object],Example:,[object Object],Women will have greater conversational memory than men,[object Object],dept. of futures studies 2010-'12,[object Object]
The Null Hypothesis,[object Object],Null Hypothesis - the absence of a relationship,[object Object],E..g., There is no difference between men’s and women’s with regards to conversational memories,[object Object],Compare observed results to Null Hypothesis,[object Object],How different are the results from the null hypothesis?,[object Object],We do not propose a null hypothesis as research hypothesis - need very large sample size / power,[object Object],Used as point of contrast for testing,[object Object],dept. of futures studies 2010-'12,[object Object]
Hypotheses testing,[object Object],When we test observed results against null:,[object Object],We can make two decisions:,[object Object],1. Accept the null,[object Object],No significant relationship,[object Object],Observed results similar to the Null Hypothesis,[object Object],2. Reject the null,[object Object],Significant relationship,[object Object],Observed results different from the Null Hypothesis,[object Object],Whichever decision, we risk making an error,[object Object],dept. of futures studies 2010-'12,[object Object]
Type I and Type II Error,[object Object],1. Type I Error,[object Object],Reality:  No relationship,[object Object],Decision:  Reject the null,[object Object],Believe your research hypothesis have received support when in fact you should have disconfirmed it,[object Object],Analogy: Find an innocent man guilty of a crime,[object Object],2. Type II Error,[object Object],Reality:  Relationship,[object Object],Decision: Accept the null,[object Object],Believe your research hypothesis has not received support when in fact you should have rejected the null.,[object Object],Analogy: Find a guilty man innocent of a crime,[object Object],dept. of futures studies 2010-'12,[object Object]
Potential outcomes of testing,[object Object],						Decision,[object Object],Accept NullReject Null,[object Object],R	No ,[object Object],E		Relationship,[object Object],A,[object Object],L,[object Object],I		,[object Object],T,[object Object],Y		Relationship,[object Object],Correct,[object Object],decision,[object Object],Type I Error ,[object Object],Correct,[object Object],decision,[object Object],Type II Error ,[object Object],dept. of futures studies 2010-'12,[object Object]
Start by setting level of risk of making a Type I Error,[object Object],How dangerous is it to make a Type I Error:,[object Object],What risk is acceptable?:,[object Object],5%? ,[object Object],1%?,[object Object],.1%?                                                             ,[object Object],Smaller percentages are more conservative in guarding against a Type I Error,[object Object],Level of acceptable risk is called “Significance level” :,[object Object],Usually the cutoff - <.05,[object Object],dept. of futures studies 2010-'12,[object Object]
Steps in Hypothesis Testing,[object Object], State research hypothesis,[object Object], State null hypothesis,[object Object],Decide the appropriate test criterion( eg. t test, χ2 test, F test etc.),[object Object],Set significance level (e.g., .05 level),[object Object], Observe results,[object Object], Statistics calculate probability of results if null hypothesis were true,[object Object], If probability of observed results is less than significance level, then reject the null,[object Object],dept. of futures studies 2010-'12,[object Object]
Guarding against  Errors,[object Object],Significance level regulates Type I Error,[object Object],Conservative standards reduce Type I Error:,[object Object],.01 instead of .05, especially with large sample,[object Object],Reducing the probability of Type I Error:,[object Object],Increases the probability of Type II Error,[object Object],Sample size regulates Type II Error,[object Object],The larger the sample, the lower the probability of Type II Error occurring in conservative testing,[object Object],dept. of futures studies 2010-'12,[object Object]
Methods used to test hypothesis,[object Object],[object Object]
Z test
F test
χ2test
……..dept. of futures studies 2010-'12,[object Object]
Testing hypothesis for two nominal variables,[object Object],Variables	Null hypothesis		Procedure,[object Object],Gender		,[object Object],				Passing is not		 Chi-square,[object Object],				related to gender		,[object Object],Pass/Fail,[object Object],dept. of futures studies 2010-'12,[object Object]
Testing hypothesis for one nominal and one ratio variable,[object Object],Variables		Null hypothesis		Procedure,[object Object],Gender		,[object Object],					Score is not		T-test,[object Object],					related to gender		,[object Object],Test score,[object Object],dept. of futures studies 2010-'12,[object Object]
Testing hypothesis for one nominal and one ratio variable,[object Object],Variable		Null hypothesis 			Procedure,[object Object],Year in school		,[object Object],				Score is not		,[object Object],				related to year in		ANOVA,[object Object],				school	,[object Object],Test score,[object Object],Can be used when nominal variable has more than two categories and can include more than one independent variable,[object Object],dept. of futures studies 2010-'12,[object Object]
Testing hypothesis for two ratio variables,[object Object],Variable		Null hypothesis	Procedure,[object Object],Hours spent		,[object Object],studying		Score is not		,[object Object],				          related to hours	          Correlation,[object Object],				          spent studying	,[object Object],Test score,[object Object],dept. of futures studies 2010-'12,[object Object]
Testing hypothesis for more than two ratio variables,[object Object],Variable		Null hypothesis		     Procedure,[object Object],Hours spent	,[object Object],studying 		Score is positively	,[object Object],				 related to hours		,[object Object],Classes 		spent studying and	       Multiple 	,[object Object],missed 		negatively related	       regression,[object Object],				to classes missed,[object Object],Test score,[object Object],dept. of futures studies 2010-'12,[object Object]
Chi square (χ2 ) test,[object Object],dept. of futures studies 2010-'12,[object Object]
Used to:,[object Object],Test for goodness of fit,[object Object],Test for independence of attributes,[object Object],Testing homogeneity,[object Object],Testing given population variance,[object Object],dept. of futures studies 2010-'12,[object Object]
Chi-Square Test of Independence,[object Object],dept. of futures studies 2010-'12,[object Object]
Introduction (1),[object Object],We often have occasions to make comparisons between two characteristics of something to see if they are linked or related to each other.,[object Object],One way to do this is to work out what we would expect to find if there was no relationship between them (the usual null hypothesis) and what we actually observe.,[object Object],dept. of futures studies 2010-'12,[object Object]
Introduction (2),[object Object],The test we use to measure the differences between what is observed and what is expected according to an assumed hypothesis is called the chi-square test.,[object Object],dept. of futures studies 2010-'12,[object Object]
For Example,[object Object],Some null hypotheses may be:,[object Object],‘there is no relationship between the subject of first period and the number of students absent in our class’.,[object Object],‘there is no relationship between the height of the land and the vegetation cover’.,[object Object],‘there is no connection between the size of farm and the type of farm’,[object Object],dept. of futures studies 2010-'12,[object Object]
Important,[object Object],The chi square test can only be used on data that has the following characteristics:,[object Object],The frequency data must have a precise numerical value and must be organised into categories or groups.,[object Object],The data must be in the form of frequencies,[object Object],The expected frequency in any one cell of the table must be greater than 5. ,[object Object],The total number of observations must be greater than 20.,[object Object],dept. of futures studies 2010-'12,[object Object]
Contingency table,[object Object],Frequency table  in which a sample from a population is  classified according to two attributes, which are divided in to two or more classes,[object Object],dept. of futures studies 2010-'12,[object Object]
Degrees of Freedom,[object Object],[object Object]
Number of cells – no. of constraints dept. of futures studies 2010-'12,[object Object]
Formula,[object Object],χ2 = ∑ (O – E)2,[object Object],E,[object Object],χ2 = The value of chi square,[object Object],O = The observed value,[object Object],E = The expected value,[object Object],∑ (O – E)2 = all the values of (O – E) squared then added together,[object Object],dept. of futures studies 2010-'12,[object Object]

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